Joint Discrete Random Variables
1 hr 42 min 6 Examples
- Introduction to Video: Joint Probability for Discrete Random Variables
- Overview and formulas of Joint Probability for Discrete Random Variables
- Consider the joint probability mass function and find the probability (Example #1)
- Create a joint probability distribution, joint marginal distribution, mean and variance, probability, and determine independence (Example #2)
- Create a joint pmf and determine mean, conditional distributions and probability (Example #3)
- Determine the joint probability distribution and marginal distribution and find probability (Example #4)
- Determine probability for travel routes and time between cities (Example #5)
- Find the joint probability function, distribution, and desired probability using the multivariate hypergeometric random variable (Example #6)
Joint Continuous Random Variables
2 hr 32 min 7 Examples
- Introduction to Video: Joint Probability for Continuous Random Variables
- Overview of Joint and Bivariate Probability Distribution and Formulas with Example #1
- Consider the joint density function on the triangle with given vertices (Example #2)
- How to find Marginal distribution and Conditional distributions with Example #3
- Find the probability of the joint distribution using a triple integral (Example #4)
- Overview of Mean and Variance and Independence for Continuous Joint Probability Distributions
- Find the marginals and conditional mean for the joint distribution (Example #5)
- Find the marginal cdf, marginal pdf, and conditional probability (Example #6)
- Find the expected values for X and Y, marginals for X and Y, and conditional probability (Example #7)
Covariance vs Correlation
1 hr 29 min 7 Examples
- Introduction to Video: Covariance and Correlation
- Review of variance for discrete and continuous random variables with Examples #1-2
- How do we find covariance?
- Find the covariance of two discrete random variables (Example #3)
- Find the covariance of two continuous random variables (Example #4)
- Determine the covariance and correlation for a joint probability distribution (Example #5)
- Find the covariance and correlation given a continuous joint density function (Example #6)
- Find the correlation for the joint probability mass function (Example #7)
Linear Combination of Random Variables
1 hr 40 min 9 Examples
- Introduction to Video: Linear Combinations of Random Variables
- Properties of Linear Combination of Random Variables
- Find the expected value and probability of the linear combination (Examples #1-2)
- Determine the expected value of the linear combination for continuous and discrete random variables (Examples #3-4)
- Find the expected value, variance and probability for the given linear combination (Examples 5-6)
- Find the expected value for the given density functions (Examples #7-8)
- Determine if the random variables are independent (Example #9-a)
- Find the expected value of the linear combination (Example #9-b)
- Find the variance and covariance of the linear combination (Example #9-c)
Chebyshev Inequality
58 min 6 Examples
- Introduction to Video: Chebyshevs Inequality
- What is Chebyshev’s Theorem? with Example #1
- Use Tchebysheff’s inequality to approximate the probability (Examples #2-3)
- Find the probability using Chebyshev’s inequality (Examples #4-5)
- Show the accuracy of Chebyshev’s Theorem (Example #6)
Chapter Test
2 hr 5 min 10 Practice Problems
- Find the probability for the discrete joint distribution (Problem #1)
- Find the marginal density and probability for the continuous joint distribution (Problem #2)
- Find the conditional distribution, expected value, and variance for the discrete joint density function (Problem #3)
- Find the marginal density functions and probability of the joint probability (Problem #4)
- Find the covariance of the joint probability density function (Problem #5)
- Determine the expected value, correlation, and linear combination for the continuous joint density function (Problem #6)
- Find the variance and demonstrate Chebyshev’s inequality (Problem #7)
- Determine the probability given a continuous joint density function (Problem #8)
- Find the cumulative density function for the random variables (Problem #9)
- Use the discrete joint probability function to find the marginal density, expected value, variance, and conditional expectancy and variance (Problem #10)